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Popular >

extreme e^{x^2-7x-1}

Solution

extreme points

e^{x^{2} - 7 x - 1}

Solution

Minimum (\frac{7}{2}, \frac{1}{e ^{\frac{53}{4}}})

Solution steps

f^{'} (x) = e^{x^{2} - 7 x - 1} (2 x - 7)

Find intervals:

Decreasing

: - \infty < x < \frac{7}{2},

Increasing

: \frac{7}{2} < x < \infty

Plug

x = \frac{7}{2}

into

e^{x^{2} - 7 x - 1} : \frac{1}{e ^{\frac{53}{4}}}

Minimum (\frac{7}{2}, \frac{1}{e ^{\frac{53}{4}}})

Popular Examples

extreme f(x,y)=5-2x+4y-x^2-4y^2 extreme points

f (x, y) = 5 - 2 x + 4 y - x^{2} - 4 y^{2}

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f (x, y) = - x^{2} + y^{2}

extreme f(x)=y^2-x^2 extreme points

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extreme f(x,y)=(x^2y)/2-xy+y^2 extreme points

f (x, y) = \frac{x ^{2} y}{2} - x y + y^{2}

Frequently Asked Questions (FAQ)

What is the extreme e^{x^2-7x-1} ?
The extreme e^{x^2-7x-1} is Minimum(7/2 , 1/(e^{53/4)})